SOLUTION: If a + b is less than c + d , and d + e is less than a + b , then e is A)less than c B) equal to c C) less than d D) greater than d

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Question 275091: If a + b is less than c + d , and d + e is less than a + b , then e is

A)less than c B) equal to c C) less than d D) greater than d

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
If a + b is less than c + d , and d + e is less than a + b , then e is

d + e < a + b and a + b < c + d implies by transitivity  of < that

d + e < c + d

Subtract d from both sides

e < c

which is choice A).

But we must rule out the fact that none of the other is ALWAYS
true.

We can rule out B), C) and D) with just one case

a=5, b=1, c=5, d=2, e=2

5 1 5 2 2   b) c) d)

A)less than c   B) equal to c   C) less than d   D) greater than d

 a + b  is less than c + d , and d + e is less than a + b 
 5 + 1  is less than 5 + 2 , and 2 + 2 is less than 5 + 1
   6    is less than   7   , and   4   is less than   6

yet B) is not true since e=2 is not equal to c=5

also C) is not true since e=2 is not less than d=2

also D) is not true since e=2 is not greater than d=2 

In fact, it can be shown that B) and D) are NEVER true, 

and that C) is only sometimes true.  

Edwin